System and method of predicting problematic areas for lithography in a circuit design

ABSTRACT

A system and method is provided which predicts problematic areas for lithography in a circuit design, and more specifically, which uses modeling data from a modeling tool to accurately predict problematic lithographic areas. The method includes identifying surface heights of plurality of tiles of a modeled wafer, and mathematically mimicking a lithographic tool to determine best planes of focus for exposure for the plurality of tiles.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a divisional application of U.S. applicationSer. No. 13/517,811, filed Jun. 14, 2012, which is a continuationapplication of U.S. application Ser. No. 13/080,148, filed on Apr. 5,2011, now U.S. Pat. No. 8,239,789, which is a divisional application ofU.S. application Ser. No. 12/104,585, filed on Apr. 17, 2008, now U.S.Pat. No. 8,001,495, the contents of each are incorporated by referenceherein in their entirety.

FIELD OF THE INVENTION

The present invention generally relates to a system and method ofpredicting problematic areas for lithography in a circuit design, andmore specifically, to a system and method which uses modeling data froma modeling tool to accurately predict problematic lithographic areas.

BACKGROUND OF THE INVENTION

Today's complex semiconductor chips can have ten or more levels ofmetallization. Since some degree of surface non-planarity is typicallyintroduced at each level, the surface non-planarity, in general, willbecome greater as more metal levels are fabricated. A three dimensionalsurface height map of one chip is shown in FIG. 1. The map shown in FIG.1 was generated using data obtained from a lithography tool prior toexposure of an upper metal level. The peak of FIG. 1 represents asurface irregularity, which represents a bad focus area. It should berecognized though, that other peaks of FIG. 1 may representirregularities in the surface, but these peaks do not necessarilyrepresent a bad area of focus as this would depend on the focal planesused by the lithography tool.

Lithography tools used today expose wafers by scanning a slit(essentially a long rectangular opening through which light passesthrough the reticle, through lens elements, and onto the wafer) acrossthe reticle field. Using optical or mechanical sensors, the lithographytool continuously reads the position of the wafer surface at multiplepoints within the slit as it scans, or reads the entire wafer surfaceprior to scanning. The tool must choose and expose with a best averagefocal plane across the slit.

Previous generation tools, e.g., single stage lithography tools, measurethe surface topography in real time, during the exposure scan, butnewer, multiple stage tools can pre-measure the entire wafer surface onthe “idle” stage prior to the exposure scan, for increased throughput.The plane of exposure can be moved up and down, and rotated around twoaxes in order to achieve the best average focal plane at any particularinstant, which is continually adjusted as the slit scans.

FIGS. 2 and 3 show two dimensional surface profiles, taken by measuringthe surface height along a surface. FIG. 2, in specific, is a twodimensional surface profile taken by measuring the surface height in adirection over the large surface “peak” in FIG. 1. (It should berecognized that the profile is not meant to be an accuraterepresentation of the surface height data and is provided forillustrative purposes only). FIG. 2 also shows a two dimensionalrepresentation of the plane, seen on edge, that the lithography toolmight choose as the best average focal plane, if it had to consider onlythis single two dimensional profile. As should be understood by those ofskill in the art, the exposure plane shown by the line in FIG. 2 can betilted (in a direction towards and away from the surface of the paper)in order to provide a better focus for some points on the surface of thewafer.

Some areas of the photoresist film which cover the wafer surface at thetime of exposure, will inevitably be in better focus than other areas.For example, point A is obviously furthest from the best average focalplane (e.g., the distance along the axis of illumination from the bestaverage focal plane), and point A will therefore have the worst averagefocus, for points along this particular profile. Point B, on the otherhand, should have much better average focus than point A. Since chipdesigns can vary widely, an infinite variety of surface profiles arepossible.

The surface topography can be modeled by empirical commercial chemicalmechanical polishing (CMP) modeling programs which take into account thedetails of the metal pattern at a particular level and also theunderlying topography from prior levels. In one example, the design datais fed into the modeling program (after model setup/calibration isperformed), and the model output is a surface height above a referencepoint, anywhere in the chip design. In this example, the surface heightis the weighted average of the average copper height and the averagedielectric height about a certain reference point. Typically the copperthickness, dielectric thickness, and surface height are mapped in termsof square regions of a specific size (tiles); although, it is understoodthat the results can be mapped and viewed in various ways.

However, current modeling cannot accurately predict all of the areasthat will be problematic for lithography. For example, currentmethodologies involve simply looking for high or low points within theCMP modeling surface height data, without taking into consideration theway in which the lithography tool decides the focal planes to use as itscans. More specifically, using the empirical modeling data andreferring back to FIG. 3, the points indicated by the arrows labeled “C”and “D” which have the same height above some reference plane, might beconsidered to be “high” points along the curve (along the surfaceprofile), at risk of bad focus (they are higher than most points alongthe curve). But because of the way that the lithography tool must selectthe best average focal plane (simulated on edge by the line labeled“Best Average Focal Plane”), the point indicated by the arrow labeled“C” will be exposed with much better focus than the point indicated bythe arrow labeled “D”. Therefore surface height alone is not necessarilyan accurate indicator of whether focus will be good or poor. Also, thepoint indicated by the arrow labeled “E” is a peak with respect to itsimmediate surroundings, yet it will be exposed with good focus.Therefore identification of such local “peaks” or “dips” is notnecessarily an accurate indicator of whether focus will be good or poor.

Accordingly, there exists a need in the art to overcome the deficienciesand limitations described hereinabove.

SUMMARY OF THE INVENTION

In a first aspect of the invention, a method of predicting problematicareas for lithography comprises identifying surface heights of aplurality of tiles of a modeled wafer; and mathematically mimicking alithographic tool to determine best planes of focus for exposure for theplurality of tiles.

In embodiments, the average distance of the surface heights of theplurality of fields of exposure for each tile is a three dimensionalrepresentation of the surface texture at a location on the modeledwafer. The identifying surface heights determines a three dimensionaltexture of the modeled wafer. The identifying is performed by a modelingtool prior to reticle and wafer fabrication. In further embodiments, themethod predicts an average distance of the surface heights of aplurality of fields of exposure for each of the plurality of tiles. Thisincludes calculating a predetermined number of focal planes for eachtile in a reticle field. Each of the predetermined number of focalplanes contributes to an equal percentage of exposure dose for an entiretile. The predetermined number of focal planes are used to measuresurface irregularity in three dimensions. The predetermined number offocal planes is different planes of exposure. Each of the plurality offields of exposure is calculated to find an average focus offset bycalculating an average distance along an axis of illumination from abest average focal plane. The method further comprises identifying tileswith an average focus offset with a value above a certain specificationdistance related to a depth of focus for a lithography process, andproviding the calculated average offset data to a mask tool.

In a further aspect of the invention, a method comprises calculating aplane which best fits modeled surface height data for a predeterminednumber of values within a slit. The method further comprises calculatinga distance along the axis of illumination distances of each tile withinthe slit from the calculated plane. The tiles which are above a certainspecification distance related to a depth of focus are identified for alithography process based on the calculated distance along the axis ofillumination.

In yet another aspect of the invention, a computer program productcomprises a computer usable medium having readable program code embodiedin the medium. The computer program product includes at least onecomponent to: identify surface heights of one or more tiles of a modeledwafer; and mathematically mimicking a lithographic tool to determinebest planes of focus for exposure for the one or more tiles

In still another aspect of the invention, a design structure is embodiedin a machine readable medium for designing, manufacturing, or testing anintegrated circuit. The design structure comprises: calculating a planewhich best fits modeled surface height data for a predetermined numberof values within a slit; calculating a distance along the axis ofillumination distances of each tile within the slit from the calculatedplane; and identifying tiles which are above a certain specificationrelated to a depth of focus for a lithography process based on thecalculated distance along the axis of illumination.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is described in the detailed description whichfollows, in reference to the noted plurality of drawings by way ofnon-limiting examples of exemplary embodiments of the present invention.

FIG. 1 shows a three dimensional surface map generated by a lithographytool prior to exposure of an upper metal level;

FIG. 2 shows a two dimensional surface profile, taken by measuring thesurface height in FIG. 1;

FIG. 3 shows a two dimensional surface profile;

FIG. 4 shows an illustrative environment for implementing features inaccordance with aspects of the invention;

FIG. 5 shows a surface model of a wafer using a conventional CMPmodeling tool;

FIG. 6 shows an exemplary lithography tool used to expose wafers byscanning a slit in accordance with the invention;

FIG. 7 shows a flow diagram implementing steps in accordance with theinvention;

FIG. 8 is an exemplary illustration of the processes in accordance withthe invention;

FIG. 9 is an exemplary circuit fabricated using the processes of theinvention; and

FIG. 10 is a flow diagram of a design process used in semiconductordesign, manufacture, and/or test.

DETAILED DESCRIPTION OF THE INVENTION

The present invention generally relates to a system and method ofpredicting problematic areas for lithography in a circuit design, andmore specifically, to a system and method which uses modeling data froma CMP modeling tool to accurately predict problematic lithographicareas. In embodiments, the system and method of the invention isconfigured to make the predictions prior to the fabrication of thereticles and/or wafers. In this way, the reticle can be fabricated usingthe data obtained thus significantly improving the features patterned onthe wafer by use of the designed reticle. The predictions can be madeusing a computing infrastructure, as discussed in greater detail below.

Illustrative Environment for Implementing Processes

FIG. 4 shows an illustrative environment 10 for managing the processesin accordance with the invention. To this extent, the environment 10includes a computer infrastructure 12 that can perform the processesdescribed herein. In particular, the computer infrastructure 12 includesa computing device 14 that comprises a tool 16, which makes computingdevice 14 operable to predict problematic areas for lithography in acircuit design.

In operation, the tool 16 (which may be in the form of software) usesCMP modeling data to predict areas of poor focus by mathematicallymimicking the way in which a stepper (lithographic tool) decides theplanes of best focus, e.g., process described herein. More specifically,the tool 16 will use the surface heights of the wafer, as modeled by theCMP modeling tool, and use this surface data to mathematically mimic theway in which the lithography tool decides its focus as it scans. Thiscan be done by, for example, taking the modeling data and predicting anaverage focus offset for each field of exposure (all tiles within aslit) in three dimensions.

For example, in operation, the tool calculates a reasonable number offocal planes, e.g., 10 focal planes, for each tile in the reticle. Inthis way, each point (focal plane) would equal a certain percentage,e.g., 10%, of the exposure dose for the entire tile. These focal planesare a reflection of the surface irregularities in three dimensions,i.e., a three dimensional surface texture of the irregularity. Once eachplane of exposure for each desired point in the reticle field iscalculated, the tool 16 finds an average focus offset by calculating theaverage distance from the planes to the wafer surface along the axis ofillumination which contribute to its exposure. The average focus offsetcan be put into a lithographic model to determine its importance suchas, for example, how the image can be printed on the wafer. A morerigorous approach can be to break the exposure into a plurality ofdifferent exposures done in rapid sequence where each is an equalpercentage of the total exposure dose and each with its own unique focussetting. The modeling can also take into account any known planarizationeffects that are due to films that are put onto the wafer after CMP butprior to lithography. For example, the films can be permanent films suchas insulator films or sacrificial films such as resists.

In embodiments, using the above data, the tool 16 will identify tileswith an average focus offset (e.g., negative or positive) with a valueabove a certain specification distance related to the depth of focus forthe lithography process. Thus, even if there is a same distance from thefocal point, the tool 16 will identify different offsets which wouldotherwise contribute to the tool being out of focus. The informationcalculated by the tool 16, e.g., offset information, can be used todesign a mask, which is used to fabricate the features on the wafer.That is, the system and method of the invention can use the informationfrom the model, calculate offset data, and provide such offset data to amask tool. In this way, the tool 16 identifies the problematic areaswhich can then be used to make a design change to the reticle. This caninclude eliminating the surface irregularities of the wafer, e.g.,eliminate the bump of FIG. 1, ensuring that a best focal plane is usedduring exposure, or widening lines or moving critical areas to name justa few design choices.

The computing device 14 includes a processor 20, a memory 22A, aninput/output (I/O) interface 24, and a bus 26. The memory 22A caninclude local memory employed during actual execution of computerprogram code, bulk storage, and cache memories which provide temporarystorage of at least some computer program code in order to reduce thenumber of times the computer program code must be retrieved from bulkstorage during execution. The program code implements the functionalityof the tool 16. Further, the computing device 14 is in communicationwith an external I/O device/resource 28 and a storage system 22B. Theexternal I/O device/resource 28 may be keyboards, displays, pointingdevices, etc.

In general, the processor 20 executes the computer program code, whichis stored in memory 22A and/or storage system 22B. While executing thecomputer program code, the processor 20 can read and/or write datato/from memory 22A, storage system 22B, and/or I/O interface 24. The bus26 provides a communications link between each of the components in thecomputing device 14. The I/O device 28 can comprise any device thatenables an individual to interact with the computing device 14 or anydevice that enables the computing device 14 to communicate with one ormore other computing devices using any type of communications link.

The computing device 14 can comprise any general purpose computingarticle of manufacture capable of executing the computer program codeinstalled thereon (e.g., a personal computer, server, handheld device,etc.). However, it is understood that the computing device 14 is onlyrepresentative of various possible equivalent computing devices that mayperform the processes described herein. To this extent, in embodiments,the functionality provided by the computing device 14 can be implementedby a computing article of manufacture that includes any combination ofgeneral and/or specific purpose hardware and/or computer program code.In each embodiment, the program code and hardware can be created usingstandard programming and engineering techniques, respectively.

Similarly, the computer infrastructure 12 is only illustrative ofvarious types of computer infrastructures for implementing theinvention. For example, in embodiments, the computer infrastructure 12comprises two or more computing devices (e.g., a server cluster) thatcommunicate over any type of communications link, such as a network, ashared memory, or the like, to perform the process described herein. Thecommunications link can comprise any combination of wired and/orwireless links; any combination of one or more types of networks (e.g.,the Internet, a wide area network, a local area network, a virtualprivate network, etc.); and/or utilize any combination of transmissiontechniques and protocols.

CMP Modeling Data and Lithographic Tool

FIG. 5 shows an exemplary surface model of a wafer using a conventionalCMP modeling tool. More specifically, FIG. 5 shows a model of surfaceheights after M4 processing; although the model can be generated for anylevel, e.g., M1 polish, M2 polish, etc. As such, the modeling tool willtake into account the details of the metal pattern at a particular leveland also the underlying topography from prior levels.

By way of explanation, design data of a chip is fed into the modelingtool (after model setup/calibration is performed), and the model outputis Cu thickness, dielectric thickness above a reference point, andsurface height above a reference point, anywhere in the chip design.Typically the copper thickness, dielectric thickness, and surface heightare mapped in terms of square regions of a specific size. In otherwords, the design is divided into a grid of squares (tiles) of a certainsize. In implementing the conventional CMP modeling tool, the averagethickness (copper), etc. is predicted for each individual tile.

The map of FIG. 5 includes the entire wafer field (chip and kerf (alsoknown as the area between chips, e.g., dicing channel)). As seen in FIG.5, there are high and low regions at the top and bottom of the field,which correspond to the kerf. It is not unusual for the kerf to have adifferent average metal density across many metal levels than theadjacent chip areas. There are also some surface height patterns visiblewithin the chip which are a reflection of the fact that there arecertain arrays or blocks within the chip that have some degree ofpattern regularity. The surface height map of FIG. 5 may be generatedprior to making the reticle or the wafer.

In implementation, the modeling data is used by the tool 16 of theinvention to predict problematic areas (and/or calculate the bestaverage focal plane for a particular slit to predict an average focusoffset for each point in the reticle field). More specifically, usingthe exemplary surface model data of FIG. 5, the tool 16 can predictareas of poor focus by mathematically mimicking the way in which thelithographic tool decides planes of best focus. That is, by using thesurface heights of the wafer, as modeled by the CMP modeling program,the tool can calculate a number of focal planes, e.g., 10 focal planes,for each tile, and use this calculated data to find an average focusoffset. This average focus offset will represent an offset in threedimensional space, providing a more accurate evaluation of focus offsetthan conventional processes which only consider a height above somereference plane.

FIG. 6 shows a highly illustrative lithography tool used to exposewafers by scanning a slit in accordance with the invention. In thisexample, the lithography tool includes a light source (lamp or laser)used to project light through a condenser lens. The condenser lensdirects the light through the reticle or mask, which contains a patternthat represents the printed circuit features. The pattern on the mask istransferred to the wafer, in the reticle field. Using the datacalculated by the tool 16, the exemplary lithography tool can scan alongthe reticle field in the direction of the arrow.

Even more specific, FIG. 7 shows an example of implementing theinvention. In this example (not to scale), a reticle field isapproximately 26×32 mm. To obtain the average focus offset for the areain the reticle field represented by area 700, the processes considerexposing this area with four different exposures, represented by thefour different focal planes shown as different lines. This area can berepresentative of a tile of different dimensions such as, for example,5×5 microns or 20×20 microns. Each of these exposures contribute onefourth of the total exposure dose. Also, each of the planes aretranslated with respect to the preceding plane by several mm; althoughin practice planes more closely spaced are contemplated by the inventionand, as such, more than four planes contributing to the exposure wouldbe provided, e.g., 10 planes or more. However, for illustrative clarityonly four focal planes are shown; whereas, perhaps 10 focal planesspaced approximately 1 mm apart (although it should be understood thatthe spacing depends on the number of planes chosen and the slit width),each contributing one tenth of the exposure dose, would be used inpractice. As those of skill in the art should understand, the more focalplanes will provide a better average focal offset. One consideration,though, is that the more focal planes would require more computationaltime.

Illustrative Processes in Accordance with the Invention

FIG. 8 shows a flow diagram implementing processes in accordance withthe invention. FIG. 8 may also represent a high level block diagramimplementing the functionality of the tool 16 shown in FIG. 4. The stepsof FIG. 8 may be implemented and executed from either a server or in aclient server relationship. Additionally, the invention can take theform of an entirely hardware embodiment, an entirely software embodimentor an embodiment containing both hardware and software elements.

In an embodiment, the invention is implemented in software, whichincludes but is not limited to firmware, resident software, microcode,etc. Furthermore, the invention can take the form of a computer programproduct accessible from a computer-usable or computer-readable mediumproviding program code for use by or in connection with a computer orany instruction execution system. The software and/or computer programproduct can be implemented in the environment of FIG. 4, as should beunderstood and capable of implementation by those of skill in the art.For the purposes of this description, a computer-usable or computerreadable medium can be any apparatus that can contain, store,communicate, propagate, or transport the program for use by or inconnection with the instruction execution system, apparatus, or device.The medium can be an electronic, magnetic, optical, electromagnetic,infrared, or semiconductor system (or apparatus or device) or apropagation medium. Examples of a computer-readable medium include asemiconductor or solid state memory, magnetic tape, a removable computerdiskette, a random access memory (RAM), a read-only memory (ROM), arigid magnetic disk and an optical disk. Current examples of opticaldisks include compact disk-read only memory (CD-ROM), compactdisk-read/write (CD-R/W) and DVD.

Referring back to FIG. 8, at step 800, the surface height values withina slit are used to calculate the plane which best fits the surfaceheight data. In embodiments, the processes will use all of the surfaceheight values from tiles within a slit to calculate focal planes,alternatively, a predetermined number of values. The calculating of theplanes can be done in much the same manner as a best straight line isdetermined to fit scattered points in two dimensions. For example,standard methods of determining and/or calculating the plane involvefinding the plane which minimizes the sum of the orthogonal distances,or the sum of the squares of the orthogonal distances, from the plane.The act of mathematically calculating the best planes mimics thelithography tool's task of deciding the planes of best focus. The methodof calculating the best planes for the surface data can be customized tomore closely approximate the method in which the lithographic toolselects the best focal planes.

At step 805, the distance from the plane to the wafer surface along theaxis of illumination for each tile is calculated (the distance can be tothe center of each tile, or to the furthest edge or corner of eachtile). This process repeats for many slits, along the reticle field. Thedistances along the axis of illumination from the tile to each focalplane which exposes it are then calculated. These distances areessentially focus offsets for each exposure. An average focus offset maythen be calculated for that particular tile. If for example, four focalplanes are used, and the focus offsets for the planes are −0.03 microns,−0.01 microns, +0.01 microns, and +0.02 microns (negative sign referringto planes below the wafer surface, and positive sign referring to planesabove the wafer surface), then the average focus offset would becalculated as: the quantity (−0.03 −0.01 +0.01 +0.02) divided by 4 (thenumber of focal planes) , which equals −0.0025 microns. All tiles withan average focus offset outside of a certain focus range (e.g.,typically spanning from some negative focus value to a some positivefocus value, with these values related to the depth of focus for thelithography process) could then be identified as potentially problematicareas for lithography.

A more rigorous method is to use a sufficiently complexphotolithographic model which could simulate the response of a resistthat is exposed to multiple (perhaps 10 or more) exposures in quicksuccession, each exposure using a different focus setting, eachcontributing an equal percentage of the total exposure dose. Asufficiently complex photolithographic model could also add someadditional random component of focus latitude to simulate additionalnonuniformities due to irregularities in the lithography tooling, waferfilms, etc. The modeling can also take into account any knownplanarization effects that are due to films that are put onto the waferafter CMP but prior to lithography. The modeled developed resist imagesof the design shapes as predicted by the photolithographic model withineach particular tile could then be examined for potential problem areas.

At step 810, all tiles are then identified which are above a certainspecification distance (related to the depth of focus for thelithography process) from the mathematical planes. In embodiments, theidentified tiles could be below or above the planes. At step 815, thesetiles are identified as design areas which will be prone to lithographyproblems at the subsequent lithography levels.

In embodiments, a more exacting method is to compute, for each tile, anaverage focus offset by calculating its average orthogonal distance frommany planes which contribute to its exposure, and identifying thosetiles with an average focus offset (be it negative or positive) with avalue above a certain specification distance which is related to thedepth of focus for the lithography process. A more rigorous approach canbe to break the exposure into a plurality of different exposures done inrapid sequence where each is an equal percentage of the total exposuredose and each with its own unique focus setting. As noted above, themodeling can also take into account any known planarization effects thatare due to films that are put onto the wafer after CMP but prior tolithography.

In step 820, the problematic tiles identified are then “fixed” bychanging the reticle design. The fixes can be made by adjusting metalpatterns/densities, in that tile and possibly in other tiles (includingdummy metal fill images), at the level at which the prediction is doneor at one or more of the underlying metal levels, and then re-runningthe check to verify that the problem tiles have been fixed. In analternate embodiment, another type of fix is to remove critical imagesin that tile (defined as images prone to poor printing when focus is offby the predicted average amount) at the next level and possibly atlevels above. In this way, such images could be moved to other tileswith smaller predicted focus offsets. The critical images could beidentified by running a separate lithographic simulation model, using asthe nominal focus values the average focus offsets for each tile asdetermined by the processes described herein, plus a random component offocus latitude, in embodiments.

Circuit and Design Structure

FIG. 9 is an exemplary circuit fabricated using the processes of theinvention. This exemplary circuit includes features 90 which correspondto the patterns on a reticle, designed with the information obtainedfrom the tool. The features will be better defined, compared toconventional system, as the reticle was in better focus to expose thepattern thereon, amongst other implementations as discussed herein.

The methods as described above are used in the fabrication of integratedcircuit chips. The resulting integrated circuit chips can be distributedby the fabricator in raw wafer form (that is, as a single wafer that hasmultiple unpackaged chips), as a bare die, or in a packaged form. In thelatter case the chip is mounted in a single chip package (such as aplastic carrier, with leads that are affixed to a motherboard or otherhigher level carrier) or in a multichip package (such as a ceramiccarrier that has either or both surface interconnections or buriedinterconnections). In any case the chip is then integrated with otherchips, discrete circuit elements, and/or other signal processing devicesas part of either (a) an intermediate product, such as a motherboard, or(b) an end product. The end product can be any product that includesintegrated circuit chips, ranging from toys and other low-endapplications to advanced computer products having a display, a keyboardor other input device, and a central processor.

FIG. 10 shows a block diagram of an exemplary design flow 900 used forexample, in semiconductor design, manufacturing, and/or test. Designflow 900 may vary depending on the type of IC being designed. Forexample, a design flow 900 for building an application specific IC(ASIC) may differ from a design flow 900 for designing a standardcomponent or from a design from 900 for instantiating the design into aprogrammable array, for example a programmable gate array (PGA) or afield programmable gate array (FPGA) offered by Altera® Inc. or Xilinx®Inc. Design structure 920 is preferably an input to a design process 910and may come from an IP provider, a core developer, or other designcompany or may be generated by the operator of the design flow, or fromother sources. Design structure 920 comprises an embodiment of theinvention as shown in FIG. 9 in the form of schematics or HDL, ahardware-description language (e.g., Verilog, VHDL, C, etc.). Designstructure 920 may be contained on one or more machine readable medium.For example, design structure 920 may be a text file or a graphicalrepresentation of an embodiment of the invention as shown in FIG. 9.Design process 910 preferably synthesizes (or translates) an embodimentof the invention as shown in FIG. 9 into a netlist 980, where netlist980 is, for example, a list of wires, transistors, logic gates, controlcircuits, I/O, models, etc. that describes the connections to otherelements and circuits in an integrated circuit design and recorded on atleast one of machine readable medium. For example, the medium may be aCD, a compact flash, other flash memory, a packet of data to be sent viathe Internet, or other networking suitable means. The synthesis may bean iterative process in which netlist 980 is resynthesized one or moretimes depending on design specifications and parameters for the circuit.

Design process 910 may include using a variety of inputs; for example,inputs from library elements 930 which may house a set of commonly usedelements, circuits, and devices, including models, layouts, and symbolicrepresentations, for a given manufacturing technology (e.g., differenttechnology nodes, 32 nm, 45 nm, 90 nm, etc.), design specifications 940,characterization data 950, verification data 960, design rules 970, andtest data files 985 (which may include test patterns and other testinginformation). Design process 910 may further include, for example,standard circuit design processes such as timing analysis, verification,design rule checking, place and route operations, etc. One of ordinaryskill in the art of integrated circuit design can appreciate the extentof possible electronic design automation tools and applications used indesign process 910 without deviating from the scope and spirit of theinvention. The design structure of the invention is not limited to anyspecific design flow.

Design process 910 preferably translates an embodiment of the inventionas shown in FIG. 9, along with any additional integrated circuit designor data (if applicable), into a second design structure 990. Designstructure 990 resides on a storage medium in a data format used for theexchange of layout data of integrated circuits and/or symbolic dataformat (e.g. information stored in a GDSII (GDS2), GL1, OASIS, mapfiles, or any other suitable format for storing such design structures).Design structure 990 may comprise information such as, for example,symbolic data, map files, test data files, design content files,manufacturing data, layout parameters, wires, levels of metal, vias,shapes, data for routing through the manufacturing line, and any otherdata required by a semiconductor manufacturer to produce an embodimentof the invention as shown in FIG. 9. Design structure 990 may thenproceed to a stage 995 where, for example, design structure 990:proceeds to tape-out, is released to manufacturing, is released to amask house, is sent to another design house, is sent back to thecustomer, etc.

While the invention has been described in terms of embodiments, those ofskill in the art will recognize that the invention can be practiced withmodifications and in the spirit and scope of the appended claims.

What is claimed is:
 1. A method, comprising: by a processor: calculatingplanes of focus for exposure for one or more tiles of a modeled waferthat best fits modeled surface height data for a predetermined number ofvalues within a slit; calculating distances of each of the tiles withinthe slit to each of the calculated planes along an axis of illumination;calculating an average focus offset from the calculated distances; andidentifying tiles with an average focus offset that is outside of acertain specification range which is related to a depth of focus for thelithography process.
 2. The method of claim 1, wherein the identifiedtiles are identified as design areas which will be prone to lithographyproblems at subsequent lithography levels.
 3. The method of claim 1,wherein the identified tiles are fixed by changing a chip design byadjusting at least one of metal patterns and densities.
 4. The method ofclaim 1, wherein the identified tiles are fixed by changing a chipdesign by adjusting at least one of metal patterns and densities inother tiles at a level at which a prediction is performed or at one ormore underlying metal levels.
 5. The method of claim 1, furthercomprising repeating the steps of claim
 1. 6. The method of claim 1,wherein critical images are removed in the identified tiles at a higherlevel.
 7. The method of claim 1, wherein the calculating the planescomprises finding a plane which minimizes a sum of the orthogonaldistances or a sum of the squares of the orthogonal distances from theplane.
 8. A memory or storage system storing computer program code thatwhen executed by a processor, causes the processor to perform a method,the method comprising: calculating planes of focus for exposure for oneor more tiles of a modeled wafer that best fits modeled surface heightdata for a predetermined number of values within a slit; calculatingdistances of each of the tiles within the slit to each of the calculatedplanes along an axis of illumination; calculating an average focusoffset from the calculated distances; and identifying tiles with anaverage focus offset that is outside of a certain specification rangewhich is related to a depth of focus for the lithography process.
 9. Thememory or storage system of claim 8, wherein the identified tiles areidentified as design areas which will be prone to lithography problemsat subsequent lithography levels.
 10. The memory or storage system ofclaim 8, wherein the identified tiles are fixed by changing a chipdesign by adjusting at least one of metal patterns and densities. 11.The memory or storage system of claim 8, wherein the identified tilesare fixed by changing a chip design by adjusting at least one of metalpatterns and densities in other tiles at a level at which a predictionis performed or at one or more underlying metal levels.
 12. The memoryor storage system of claim 8, wherein the method further comprisesrepeating the steps of claim
 8. 13. The memory or storage system ofclaim 8, wherein critical images are removed in the identified tiles ata higher level.
 14. The memory or storage system of claim 8, wherein thecalculating the planes comprise finding a plane which minimizes a sum ofthe orthogonal distances or a sum of the squares of the orthogonaldistances from the plane.